Question

❤️Hello Maths Experts❤️​

‼️Please solve the problem
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A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The
angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30º. Find the distance travelled by the balloon during the interval.​

Answer 1

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⎟⎟✪✪ QUESTION ✪✪⎟⎟

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After sometime, the angle of elevation reduces to 30º. Find the distance travelled by the balloon during the interval.

⎟⎟✪✪ ANSWER ✪✪⎟⎟

✿✿ Refer to Image first ✿✿

◆ Height of the balloon from tower = 88.2 m

◆ Height of the girl = 1.2 m

◆ Angles of elevations = 60° and 30°

◆ Let the distance travelled = d m

From the figure

tan 60° = 87/x

➜ √3 = 87/x

➜ 87 = √3 x ━━━━ ➀

➜ x = 87/√3 m

Also tan 30° = 87/x+d

➜ 1/√3 = 87/x+d

➜ 87 = x+d/√3 ━━━━ ➁

From ➀ and ➁

➜ √3x = x+d/√3

➜ √3 ᐧ √3x = x + d

➜ 3x = x + d

➜ 2x =d

Distance travelled = 2 × 87/√3

➜ 2×29×√3×√3 / √3

➜ 58√3 m

The distance travelled by the balloon during the interval = 58√3 m